Browder–Minty theorem
In mathematics, the Browder–Minty theorem (sometimes called the Minty–Browder theorem) states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each continuous linear functional g ∈ X∗, there exists a solution u ∈ X of the equation T(u) = g. (Note that T itself is not required to be a linear map.)
The theorem is named in honor of Felix Browder and George J. Minty, who independently proved it.[1]
See also
[edit]- Pseudo-monotone operator; pseudo-monotone operators obey a near-exact analogue of the Browder–Minty theorem.
References
[edit]- ^ Browder, Felix E. (1967). "Existence and perturbation theorems for nonlinear maximal monotone operators in Banach spaces". Bulletin of the American Mathematical Society. 73 (3): 322–328. doi:10.1090/S0002-9904-1967-11734-8. ISSN 0002-9904.
- Renardy, Michael & Rogers, Robert C. (2004). An introduction to partial differential equations. Texts in Applied Mathematics 13 (Second ed.). New York: Springer-Verlag. p. 364. ISBN 0-387-00444-0. (Theorem 10.49)
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